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When can one domain enclose another in 3?

Part of: Real and complex geometry General convexity Global differential geometry

Published online by Cambridge University Press:  09 April 2009

Jiazu zhou
Jiazu zhou
Affiliation:
Department of Mathematics, Temple University, Philadelphia, PA 19122, USA, e-mail: zhou@euclid.math.temple.edu
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Abstract

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In this paper, we give a sufficient condition (Theorem) in order that one domain D1 bounded by a C2-smooth boundary can be enclosed in, or enclose, another domain D0 bounded by the same kind of boundary. A same kind of sufficient condition for convex bodies (Corollary) is also obtained.

Keywords

Domainconvex bodycurvaturemean curvaturekinematic measurekinematic formulaquermassintegralscircumscribed ball.

MSC classification

Secondary: 52A22: Random convex sets and integral geometry 53C21: Methods of Riemannian geometry, including PDE methods; curvature restrictions 51M16: Inequalities and extremum problems
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 59 , Issue 2 , October 1995 , pp. 266 - 272
Copyright
Copyright © Australian Mathematical Society 1995

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